Peristaltic pumps are widely used in medical applications for the intravenous administration of various fluids. A sophisticated type of medical peristaltic pump must be able to accurately deliver fluids at a rate varying from at least 1 ml/hr to about 1,000 ml/hr. It is inherent in the nature of peristaltic pumps that because of the stroke volume in the tube being refilled, the pump must have a deadband during which no delivery of fluid takes place. Specifically, in a typical peristaltic pump, approximately 150.degree. out of each 360.degree. cycle of pump operation intervenes between the end of one measured fluid increment and the beginning of the next. If the pump is running at high speed, this deadband causes little or no problems, as the interval between fluid increments is only a few tenths of a second. If, however, the pump is running at extremely low rates, it is possible for the interval between fluid increments to become as long as several minutes. During this time, the patient receives no medication at all, and medically unacceptable conditions result.